دانلود رایگان مقاله ساخت مواد جامد بی اسپلاین از مش تتراهیدرال برای تحلیل ایزوهندسی

Abstract

With the advent of isogeometric analysis, the modeling of spline solids became an important topic. In this paper, we present a discrete volume parameterization method for tetrahedral (tet) mesh models and an iterative fitting algorithm with a B-spline solid. The discrete volume parameterization method maps the vertices of a tet mesh into a parameter domain by solving a system of linear equations. Each equation is explicitly constructed for an inner vertex in terms of the geometric information adjacent to the inner vertex. Moreover, we show the validity of the parameterization system of linear equations thus constructed. Next, because the number of tet mesh vertices is usually very large, we develop an iterative algorithm for fitting a tet mesh with a B-spline solid. The iterative algorithm exploits the geometric information of the control hexahedral (hex) mesh and the local support property of the spline function, so the total amount of computation in each iteration is unchanged when the number of control hex mesh vertices of the B-spline solid is increased. Therefore, the iterative fitting algorithm performs very well in incremental fitting of a tet mesh with a large number of vertices. Finally, four experimental examples presented in this paper show the efficiency and effectiveness of the developed algorithms.

5. Conclusion

In this paper, we developed a discrete volume parameterization method and an iterative algorithm for fitting a tet mesh model with a B-spline solid. The linear system of equations for the volume parameterization is constructed geometrically, and the method is equivalent to solving a harmonic equation by the finite element method. Therefore, the generated parameterization is guaranteed to have no self-overlapping. Moreover, we presented an iterative algorithm for fitting a tet mesh model. The iteration speed of the iterative algorithm is determined by the number of tet mesh vertices rather than the number of control hex mesh vertices of the B-spline solid. Thus, the proposed iterative algorithm is desirable in fitting a tet mesh with a large number of vertices incrementally.